LARGE GRAPH LIMIT FOR AN SIR PROCESS IN RANDOM NETWORK WITH HETEROGENEOUS CONNECTIVITY
LARGE GRAPH LIMIT FOR AN SIR PROCESS IN RANDOM NETWORK WITH HETEROGENEOUS CONNECTIVITY
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DOI：
10.1214/11-aap773
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发表时间：
2012-04-01
影响因子：
1.8
通讯作者：
Viet Chi Tran
中科院分区：
文献类型：
--
作者：
Decreusefond, Laurent;Dhersin, Jean-Stephane;Viet Chi Tran
我们考虑一个SIR流行病模型在配置模型网络上传播，其中顶点的度分布是给定的，并且边缘是随机匹配的。流行病的演变被总结为三个测量值方程，它们描述了易感个体的程度以及从感染或移除个体到易感群体的边缘数。这三种度分布足以描述疾病的病程。研究了大种群的极限。作为推论，这为Volz[数学生物学56(2008)293-310]得到的方程提供了严格的证明。
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz [Mathematical Biology 56 (2008) 293-310].